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A NEURAL MECHANISM FOR THE EMERGENCE OF NON-CRITICAL POWER LAWS - Serena Di Santo

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A NEURAL MECHANISM FOR THE EMERGENCE OF NON-CRITICAL POWER LAWS - Serena Di Santo

  1. 1. A NEURAL MECHANISM FOR THE EMERGENCE OF NON-CRITICAL POWER LAWS Serena Di Santo 21/06/2016 Lake Como School
  2. 2. tissue on array local field potentials thresholded signals A NEURAL MECHANISM FOR THE EMERGENCE OF NON-CRITICAL POWER LAWS c r i t i c a l
  3. 3. WILSON-COWAN MODEL AND BALANCED AMPLIFICATION OF FLUCTUATIONS E I wI wI wE wE @tE = ↵E + (1 E)f(s) @tI = ↵I + (1 I)f(s) f(s) = ✓[tanh(s)] s = wEE wII + h ' Benayoun M, Cowan JD, van Drongelen W, Wallace E, (2010) PLoS Comput Biol Murphy BK, Miller K, (2009) Neuron wE wI E I not balanced + p ↵E + (1 E)f(s)⌘E + p ↵I + (1 I)f(s)⌘I
  4. 4. NON NORMAL FORMS AND A NOISE INDUCED ZERO MODE Linear stability close to the fixed point… Non Diagonalizable Non orthogonal Eigenvect Define Pseudospectra ˙⇢ = a⇢ b⇢2 + h + p ⇢⌘(t) T U N N E L I N G Amplificated fluctuations +noise ☞ NON NORMAL FORM AT A 6= AAT Pst(⇢) ⇠ 1 ⇢1 2h 2
  5. 5. SIMILAR PHENOMENON, DIFFERENT REGULATORY MECHANISM: TSODYKS-MARKRAM MODEL FOR SYNAPTIC PLASTICITY ˙R = 1 ⌧ (Rm R) u⇢R⇢ b⇢2 c⇢3 + !⇢R + p ⇢⌘˙⇢ = a⇢ b⇢2 c⇢3 + h + !⇢R + p ⇢⌘ NON-NORMAL FORMS ☞AMPLIFICATION OF FLUCTUATIONS ☞ NOISE INDUCED ZERO MODE☞ ☞NON-CRITICAL POWER LAWS
  6. 6. THANKS TO MIGUEL ANGEL Muñoz & PABLO Villegas

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